The beauty of discovering some simple yet elegant proof either to something new or to an already established fact is discussed. A combinatorial problem that deals with covering a checkerboard with dominoes is presented as a starting point for individual investigation of similar problems. (MP)

Results obtained from investigating number properties are discussed, along with six points that are felt, in general, to be the ingredients necessary for a successful learning experience. Two programs written in BASIC designed to aid in aspects of Number Theory are included. (MP)

Almost-Regular Polygons (ARPs) are viewed as interesting, but hardly ever noticed. The growing availability of computers means that such figures can be examined. A program written in BASIC which was developed to generate and test large blocks of cases is presented and described. (MP)

Details are given of a simple computer program written in BASIC which calculates the sine of an angle through an application of DeMoivre's Theorem. The program is included in the material, and the program's success is discussed in terms of why the approximation works. (MP)

A program written in PASCAL designed to find the number of binary trees possible for a given number of nodes is presented. The problem was found to be highly motivating and exciting for the group of introductory computer science students with whom it was used. (MP)

A brief introduction to the broad field of curve-fitting is provided to help explain the reasoning behind least-squares data fitting, and also to provide useful equations for two functional forms of interest in chemistry. Appendices give program examples written in Fortran and detail the method of Guggenheim. (MP)

A possible logical flaw based on similar triangles is discussed with the Sherlock Holmes mystery, "The Muskgrave Ritual." The possible flaw has to do with the need for two trees to have equal growth rates over a 250-year period in order for the solution presented to work. (MP)

A method of using vector analysis is presented that is an application of calculus that helps to find the best angle for tacking a boat into the wind. While the discussion is theoretical, it is seen as a good illustration of mathematical investigation of a given situation. (MP)

Utilized is the technique of expanding circles to explore the truth of the statement that, if the sums of the lengths of the opposite sides of a quadrilateral are equal, then a circle can be inscribed within that quadrilateral. This statement is the converse of a well-known geometric theorem. (JJK)

The number theory concepts of perfect, deficient, and abundant numbers are subdivided and then utilized to discuss propositions concerning semiperfect, weird, and integer-perfect numbers. Conjectures about relationships among these latter numbers are suggested as avenues for further investigation. (JJK)

Demonstrated is the use of BASIC computer programs to simulate a binomial experiment and test a simple statistical hypothesis. The theoretical results are reached with the third programing attempt. All results, as well as computer programs, are included. (JJK)

Examined are the three regular tessellations and derived semiregular tessellations whose regular polygons meet at common vertices. Included are BASIC computer program listings that explore the various combinations of regular polygons that can form regular or semiregular tessellations. (JJK)